Question 1

The vertical spread of the data points about the regression line is measured by the y-intercept.

Accepted Answer

A) True 
 B)False

Question 2

The manager of a fast food restaurant wants to determine how sales in a given week are related to the number of discount vouchers (#) printed in the local newspaper during the week. The number of vouchers and sales ($000s) from 10 randomly selected weeks is given below with the predicted sales.
Calculate the residuals. $$\begin{array} { | c | c | c | c | } 
\hline \text { Observation } & \text { Sales } & \text { Predicted Sales } & \text { Residuals } \
\hline 1 & 12.8 & 13.4147 & - 0.6147 \
\hline 2 & 15.4 & 14.8000 & 0.6000 \
\hline 3 & 13.9 & 13.8765 & 0.0235 \
\hline 4 & 11.2 & 12.9529 & - 1.7529 \
\hline 5 & 18.7 & 20.3412 & - 1.6412 \
\hline 6 & 17.9 & 16.1853 & 1.7147 \
\hline 7 & 16.8 & 15.2618 & 1.5382 \
\hline 8 & 15.9 & 14.3382 & 1.5618 \
\hline 9 & 11.5 & 12.9529 & - 1.4529 \
\hline 10 & 13.9 & 13.8765 & 0.0235 \
\hline
\end{array}$$ Plot the residuals against the predicted values of y. Does the variance appear to be constant?

Accepted Answer

@#IMG-DLM& It appears that het

Question 3

A statistician investigating the relationship between the amount of precipitation (in inches) and the number of car accidents gathered data for 10 randomly selected days. The results are presented below. $$\begin{array} { | c | c | c | } 
\hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \
\hline 1 & 0.05 & 5 \
\hline 2 & 0.12 & 6 \
\hline 3 & 0.05 & 2 \
\hline 4 & 0.08 & 4 \
\hline 5 & 0.10 & 8 \
\hline 6 & 0.35 & 14 \
\hline 7 & 0.15 & 7 \
\hline 8 & 0.30 & 13 \
\hline 9 & 0.10 & 7 \
\hline 10 & 0.20 & 10 \
\hline
\end{array}$$ Calculate the Spearman rank correlation coefficient, and test to determine at the 5% significance level whether we can infer that a linear relationship exists between the number of accidents and the amount of precipitation.

Accepted Answer

@#IMG-DLM& 0.896. H_o: F1F1F1S1F1F1F10s =

Question 4

A financier whose specialty is investing in movie productions has observed that, in general, movies with 'big-name' stars seem to generate more revenue than those movies whose stars are less well known. To examine his belief, he records the gross revenue and the payment (in $ million) given to the two highest-paid performers in the movie for 10 recently released movies. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ Use the predicted and actual values of y to calculate the residuals.

Accepted Answer

@#IMG-DLM& : -0.137, 1.122, 3.

Question 5

The standard error of estimate, $S _ { ? }$ , is a measure of:

Accepted Answer

A) variation of y around the regression line. 
B) variation of x around the regression line. 
C) variation of y around the mean $\bar { y }$ . 
D) variation of x around the mean $\bar { x }$ . 
A) variation of y around the regression line. 
B) variation of x around the regression line. 
C) variation of y around the mean $\bar { y }$ . 
D) variation of x around the mean $\bar { x }$ .

Question 6

A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100 000 of population and the average daily sunshine in eight country towns around NSW. These data are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Average daily sunshine (hours) } & 5 & 7 & 6 & 7 & 8 & 6 & 4 & 3 \
\hline \text { Skin cancer per } 100000 & 7 & 11 & 9 & 12 & 15 & 10 & 7 & 5 \
\hline
\end{array}$$ Calculate the standard error of estimate, and describe what this statistic tells you about the regression line.

Accepted Answer

se = 0.960

Question 7

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is:

Accepted Answer

A) 80%. 
B) 0.64%. 
C) -80%. 
D) 64% 
A) 80%. 
B) 0.64%. 
C) -80%. 
D) 64%

Question 8

A financier whose specialty is investing in movie productions has observed that, in general, movies with 'big-name' stars seem to generate more revenue than those movies whose stars are less well known. To examine his belief, he records the gross revenue and the payment (in $ million) given to the two highest-paid performers in the movie for 10 recently released movies. $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of two highest- } \
\text { paid performers } ( \$ \mathrm {~m} )
\end{array} & \begin{array} { c } 
\text { Gross revenue } \
( \$ \mathrm {~m} )
\end{array} \
\hline 1 & 5.3 & 48 \
\hline 2 & 7.2 & 65 \
\hline 3 & 1.3 & 18 \
\hline 4 & 1.8 & 20 \
\hline 5 & 3.5 & 31 \
\hline 6 & 2.6 & 26 \
\hline 7 & 8.0 & 73 \
\hline 8 & 2.4 & 23 \
\hline 9 & 4.5 & 39 \
\hline 10 & 6.7 & 58 \
\hline
\end{array}$$ Predict with 95% confidence the average gross revenue of a movie whose top two stars earn $5.0 million.

Accepted Answer

45.65 ± 1.

Question 9

If the standard error of estimate $S _ { \varepsilon }$ = 20 and n = 8, then the sum of squares for error, SSE, is 2400.

Accepted Answer

A) True 
 B)False

Question 10

In a regression problem, if the coefficient of determination is 0.95, this means that:

Accepted Answer

A) 95% of the y values are positive. 
B) 95% of the variation in y can be explained by the variation in x. 
C) 95% of the x values are equal. 
D) 95% of the variation in x can be explained by the variation in y. 
A) 95% of the y values are positive. 
B) 95% of the variation in y can be explained by the variation in x. 
C) 95% of the x values are equal. 
D) 95% of the variation in x can be explained by the variation in y.

Question 11

When the variance, $\sigma _ { \varepsilon } ^ { 2 }$ , of the error variable $\varepsilon$ is a constant no matter what the value of x is, this condition is called:

Accepted Answer

A) homocausality. 
B) heteroscedasticity. 
C) homoscedasticity. 
D) heterocausality. 
A) homocausality. 
B) heteroscedasticity. 
C) homoscedasticity. 
D) heterocausality.

Question 12

Plot the residuals against the predicted values of y. Does the variance appear to be constant?

Accepted Answer

@#IMG-DLM& It appears that het

Question 13

An economist wanted to analyse the relationship between the speed of a car (x) in kilometres per hour (kmph) and its fuel consumption (y) in kilometres per litre (kmpl). In an experiment, a car was operated at several different speeds and for each speed the fuel consumption was measured. The data obtained are shown below. $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \text { Speed (mph) } & 25 & 35 & 45 & 50 & 60 & 65 & 70 \
\hline \begin{array} { l } 
\text { Fuel consumtion } \
\text { (mpg) }
\end{array} & 40 & 39 & 37 & 33 & 30 & 27 & 25 \
\hline
\end{array}$$ a. Find the least squares regression line.
b. Calculate the standard error of estimate, and describe what this statistic tells you about the regression line.
c. Do these data provide sufficient evidence at the 5% significance level to infer that a linear relationship exists between higher speeds and lower fuel consumption?
d. Predict with 99% confidence the fuel consumption of a car traveling at 55 kmph.

Accepted Answer

a. @#IMG-DLM& = 50.6563 - 0.3531x.
b. se = 1.448;

Question 14

Pop-up coffee vendors have been popular in the city of Adelaide in 2013. A vendor is interested in knowing how temperature (in degrees Celsius) impacts daily hot coffee sales revenue (in $00's).
A random sample of 6 days was taken, with the daily hot coffee sales revenue and the corresponding temperature of that day noted. Excel output given below. $$\begin{array} { | c | c | } 
\hline \text { Coffee sales revenue } & \text { Temperature } \
\hline 6.50 & 25 \
\hline 10.00 & 17 \
\hline 5.50 & 30 \
\hline 4.50 & 35 \
\hline 3.50 & 40 \
\hline 28.00 & 9 \
\hline
\end{array}$$ $\begin{array}{|l|r|c|c|c|r|r|}
\hline \text { SUMMARY OUTPUT } & & \
\hline \text { RegressionStatistios } & & \
\hline \text { Multiple R } & 0.8644 & \
\hline \text { RSquare } & 0.7472 & \
\hline \text { Adjusted RSquare } & 0.6840 & \
\hline \text { Standard Error } & 5.2027 & \
\hline \text { Observations } & 6 & \\hline\
\hline \text { ANOVA } & & & & & & \
\hline & d f & S S & M S & F & \text { Significance } F & \
\hline \text { Regression } & 1 & 320.0617 & 320.0617 & 11.8244 & 0.0263 & \
\hline \text { Residual } & 4 & 108.2716 & 27.0679 & & & \
\hline \text { Total } & 5 & 4283333 & & & & \\hline\
\hline & \text { Coefficient } & \text { StandardError } &{\text { tStat }} & \text { P-value } & \text { Lover 95\% } & {\text { Upper 95\% }} \
\hline \text { Intercept } & 27.7179 & 5.6629 & 4.8946 & 0.0081 & 11.9952 & 43.4406 \
\hline \text { Temperature } & -0.6943 & 0.2019 & -3.4387 & 0.0263 & -1.2549 & -0.1337 \
\hline
\end{array}$ Test the hypothesis that the population intercept is positive, at the 5% level of significance.

Accepted Answer

H_o: β₀ = 0 H_A: β₀ > 0 p-value = (0

Question 15

Given that cov(x,y) = 10, $s _ { y } ^ { 2 }$ = 15, $S _ { x } ^ { 2 }$ = 8 and n = 12, the value of the standard error of estimate, $S _ { \varepsilon }$ , is 2.75.

Accepted Answer

A) True 
 B)False

Question 16

A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100 000 of population and the average daily sunshine in eight country towns around NSW. These data are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Average daily sunshine (hours) } & 5 & 7 & 6 & 7 & 8 & 6 & 4 & 3 \
\hline \text { Skin cancer per } 100000 & 7 & 11 & 9 & 12 & 15 & 10 & 7 & 5 \
\hline
\end{array}$$ Calculate the coefficient of determination and interpret it.

Accepted Answer

@#IMG-DLM& 0.9231. This means that 92.31

Question 17

The quality of oil is measured in API gravity degrees - the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field, who believes that there is a relationship between quality and price per barrel. $$\begin{array} { | c | c | } 
\hline \text { Oil degrees API } & \text { Price per barrel (in } \$ \text { ) } \
\hline 27.0 & 12.02 \
\hline 28.5 & 12.04 \
\hline 30.8 & 12.32 \
\hline 31.3 & 12.27 \
\hline 31.9 & 12.49 \
\hline 34.5 & 12.70 \
\hline 34.0 & 12.80 \
\hline 34.7 & 13.00 \
\hline 37.0 & 13.00 \
\hline 41.0 & 13.17 \
\hline 41.0 & 13.19 \
\hline 38.8 & 13.22 \
\hline 39.3 & 13.27 \
\hline
\end{array}$$ A partial computer output follows.
Descriptive Statistics $$\begin{array} { | l | r | r | r | r | } 
\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \
\hline \text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \
\hline \text { Frice } & 13 & 12.730 & 0.457 & 0.127 \
\hline
\end{array}$$ Covariances $$\begin{array} { | l | r | r | } 
\hline & \text { Degrees } & \text { Price } \
\hline \text { Degrees } & 21.281667 & \
\hline \text { Price } & 2.026750 & 0.208833 \
\hline
\end{array}$$ Regression Analysis $$\begin{array} { | l | r | r | r | r | } 
\hline \text { Fredictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \
\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \
\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \
\hline
\end{array}$$ S = 0.1314 R-Sq = 92.46% R-Sq(adj) = 91.7%
Analysis of Variance $$\begin{array} { | l | r | r | r | r | r | } 
\hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \mathrm { F } & \mathrm { P } \
\hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \
\hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \
\hline \text { Total } & 12 & 2.5060 & & & \
\hline
\end{array}$$ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between the quality of oil and price per barrel.

Accepted Answer

H₀: β₁ = 0 H_A: β₁ ≠ 0 Rejection re

Question 18

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line $\hat { y }$ = 75 +6x. This implies that if $800 is spent on advertising, then the predicted amount of sales (in dollars) is:

Accepted Answer

A) $4875. 
B) $123 000. 
C) $487 500. 
D) $12 300. 
A) $4875. 
B) $123 000. 
C) $487 500. 
D) $12 300.

Question 19

A regression analysis between height y (in cm) and age x (in years) of 2 to 10 years old boys yielded the least squares line $\hat { y }$ = 87 + 6.5x. This implies that by each additional year height is expected to:

Accepted Answer

A) increase by 93.5cm. 
B) increase by 6.5cm. 
C) increase by 87cm. 
D) decrease by 6.5cm. 
A) increase by 93.5cm. 
B) increase by 6.5cm. 
C) increase by 87cm. 
D) decrease by 6.5cm.

Question 20

If the coefficient of determination is 81%, and the linear regression model has a negative slope, what is the value of the coefficient of correlation?

Accepted Answer

A) − 0.81 
B) 0.90 
C) 0.81 
D) −0.90 
A) − 0.81 
B) 0.90 
C) 0.81 
D) −0.90

The vertical spread of the data points about the regression line is measured by the y-intercept.

The standard error of estimate, $S _ { ? }$ , is a measure of:

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is:

If the standard error of estimate $S _ { \varepsilon }$ = 20 and n = 8, then the sum of squares for error, SSE, is 2400.

In a regression problem, if the coefficient of determination is 0.95, this means that:

When the variance, $\sigma _ { \varepsilon } ^ { 2 }$ , of the error variable $\varepsilon$ is a constant no matter what the value of x is, this condition is called:

Plot the residuals against the predicted values of y. Does the variance appear to be constant?

Given that cov(x,y) = 10, $s _ { y } ^ { 2 }$ = 15, $S _ { x } ^ { 2 }$ = 8 and n = 12, the value of the standard error of estimate, $S _ { \varepsilon }$ , is 2.75.

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line $\hat { y }$ = 75 +6x. This implies that if $800 is spent on advertising, then the predicted amount of sales (in dollars) is:

A regression analysis between height y (in cm) and age x (in years) of 2 to 10 years old boys yielded the least squares line $\hat { y }$ = 87 + 6.5x. This implies that by each additional year height is expected to:

If the coefficient of determination is 81%, and the linear regression model has a negative slope, what is the value of the coefficient of correlation?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Multiple Regression

Time-Series Analysis and Forecasting

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Exam 15: Simple Linear Regression and Correlation

The vertical spread of the data points about the regression line is measured by the y-intercept.

The standard error of estimate, S?S _ { ? }S?​ , is a measure of:

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is:

If the standard error of estimate SεS _ { \varepsilon }Sε​ = 20 and n = 8, then the sum of squares for error, SSE, is 2400.

In a regression problem, if the coefficient of determination is 0.95, this means that:

When the variance, σε2\sigma _ { \varepsilon } ^ { 2 }σε2​ , of the error variable ε\varepsilonε is a constant no matter what the value of x is, this condition is called:

Plot the residuals against the predicted values of y. Does the variance appear to be constant?

Given that cov(x,y) = 10, sy2s _ { y } ^ { 2 }sy2​ = 15, Sx2S _ { x } ^ { 2 }Sx2​ = 8 and n = 12, the value of the standard error of estimate, SεS _ { \varepsilon }Sε​ , is 2.75.

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line y^\hat { y }y^​ = 75 +6x. This implies that if $800 is spent on advertising, then the predicted amount of sales (in dollars) is:

A regression analysis between height y (in cm) and age x (in years) of 2 to 10 years old boys yielded the least squares line y^\hat { y }y^​ = 87 + 6.5x. This implies that by each additional year height is expected to:

If the coefficient of determination is 81%, and the linear regression model has a negative slope, what is the value of the coefficient of correlation?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

The standard error of estimate, $S _ { ? }$ , is a measure of:

If the standard error of estimate $S _ { \varepsilon }$ = 20 and n = 8, then the sum of squares for error, SSE, is 2400.

When the variance, $\sigma _ { \varepsilon } ^ { 2 }$ , of the error variable $\varepsilon$ is a constant no matter what the value of x is, this condition is called:

Given that cov(x,y) = 10, $s _ { y } ^ { 2 }$ = 15, $S _ { x } ^ { 2 }$ = 8 and n = 12, the value of the standard error of estimate, $S _ { \varepsilon }$ , is 2.75.

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line $\hat { y }$ = 75 +6x. This implies that if $800 is spent on advertising, then the predicted amount of sales (in dollars) is:

A regression analysis between height y (in cm) and age x (in years) of 2 to 10 years old boys yielded the least squares line $\hat { y }$ = 87 + 6.5x. This implies that by each additional year height is expected to: